Abstract
A phase map can be obtained from the real and imaginary components of a complex valued magnetic resonance (MR) image. Many applications, such as MR phase velocity mapping and susceptibility mapping, make use of the information contained in the MR phase maps. Unfortunately, noise in the complex MR signal affects the measurement of parameters related to phase (e.g, the phase velocity). In this paper, we propose a nonlocal maximum likelihood (NLML) estimation method for enhancing phase maps. The proposed method estimates the true underlying phase map from a noisy MR phase map. Experiments on both simulated and real data sets indicate that the proposed NLML method has a better performance in terms of qualitative and quantitative evaluations when compared to state-of-the-art methods.
Similar content being viewed by others
References
Aja-Fernández, S., Alberola-López, C., Westin, C.: Noise and signal estimation in magnitude MRI and Rician distributed images: a LMMSE approach. IEEE Trans. Image Process. 17, 1383–1398 (2008)
Bioucas-Dias, J., Katkovnik, V., Astola, J., Egiazarian, K.: Absolute phase estimation: adaptive local denoising and global unwrapping. Appl. Opt. 47(29), 5358–5369 (2002)
Bonny, J.M., Renou, J.P., Zanca, M.: Optimal measurement of magnitude and phase from MR data. J. Magn. Reson. Ser. B 113(2), 136–144 (1996)
Buades, A., Coll, B., Morel, J.M.: A review of image denoising algorithms, with a new one. Multiscale Model. Simul. 4, 490–530 (2005)
Chavez, S., Xiang, Q.S., An, L.: Understanding phase maps in MRI: a new cutline phase unwrapping method. IEEE Trans. Med. Imaging 21(8), 966–977 (2002)
Cruz-EnrÃquez, H., Lorenzo-Ginori, J.: Combined wavelet and nonlinear filtering for MRI phase images. In: Kamel, M., Campilho, A. (eds.) Image Analysis and Recognition, Lecture Notes in Computer Science, vol. 5627, pp 83–92. Springer, Berlin (2009). iSBN: 978-3-642-02610-2
den Dekker, A.J., Sijbers, J.: Data distributions in magnetic resonance images: a review. Phys. Med. 30(7), 725–741 (2014)
Fisher, Y.: Pixelized Data. Springer, London (1995)
He, L., Greenshields, I.R.: A nonlocal maximum likelihood estimation method for Rician noise reduction in MR images. IEEE Trans. Med. Imaging 28, 165–172 (2009)
Heydari, M., Karami, M.R., Babakhani, A.: A new adaptive coupled diffusion PDE for MRI Rician noise. Signal Image Video Process. 10(7), 1–8 (2016)
ISMRM (2010) http://www.ismrm.org/mri_unbound/simulated.htm
Krissian, K., Aja-Fernández, S.: Noise-driven anisotropic diffusion filtering of MRI. IEEE Trans. Image Process. 18(10), 2265–2274 (2009)
Lorenzo-Ginori, J.V., Plataniotis, K.N., Venetsanopoulos, A.N.: Nonlinear filtering for phase image denoising. IEEE Proc. Vis. Image Signal Process. 149(5), 290–296 (2002)
Manjón, J.V., Carbonell-Caballero, J., Lull, J.J., García-Martí, G., Martí-Bonmatí, L., Robles, M.: Mri denoising using non-local means. Med. Image Anal. 12(4), 514–523 (2008)
Mohan, J., Krishnaveni, V., Guo, Y.: A survey on the magnetic resonance image denoising methods. Biomed. Signal Process. Control 9, 56–69 (2014)
Rajan, J., Poot, D., Juntu, J., Sijbers, J.: Noise measurement from magnitude MRI using local estimates of variance and skewness. Phys. Med. Biol. 55, N441–N449 (2010)
Rajan, J., Jeurissen, B., Verhoye, M., Van Audekerke, J., Sijbers, J.: Maximum likelihood estimation-based denoising of magnetic resonance images using restricted local neighborhoods. Phys. Med. Biol. 56, 5221–5234 (2011)
Rajan, J., Van Audekerke, J., Van der Linden, A., Verhoye, M., Sijbers, J.: An adaptive non local maximum likelihood estimation method for denoising magnetic resonance images. In: 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI), pp 1136–1139. IEEE (2012)
Rajan, J., Veraart, J., Van Audekerke, J., Verhoye, M., Sijbers, J.: Nonlocal maximum likelihood estimation method for denoising multiple coil magnetic resonance images. Magn. Reson. Imaging 30(10), 1512–1518 (2012b)
Rajan, J., den Dekker, A.J., Sijbers, J.: A new non-local maximum likelihood estimation method for Rician noise reduction in magnetic resonance images using the Kolmogorov–Smirnov test. Signal Proc. 103, 16–23 (2014)
Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Automated unwrapping of MR phase images applied to BOLD MR venography at 3 Tesla. Magn. Reson. Imaging 18(2), 175–180 (2003)
Rauscher, A., Barth, M., Reichenbach, J.R., Stollberger, R., Moser, E.: Magnetic susceptibility-weighted MR phase imaging of the human brain. J. Neuroradiol. 26(4), 736–742 (2005)
Riji, R., Rajan, J., Sijbers, J., Nair, M.S.: Iterative bilateral filter for Rician noise reduction in MR images. Signal Image Video Process. 9(7), 1543–1548 (2015)
Sharif, M., Hussain, A., Jaffar, M.A., Choi, T.S.: Fuzzy-based hybrid filter for Rician noise removal. Signal Image and Video Process. 10(2), 215–224 (2016)
Sijbers, J., den Dekker, A.J., Scheunders, P., Van Dyck, D.: Maximum likelihood estimation of Rician distribution parameters. IEEE Trans. Med. Imaging 17(3), 357–361 (1998)
Acknowledgements
This work was partially supported by the Research Foundation-Flanders (FWO, Belgium) through project funding G037813N and the TOP BOF project University of Antwerp (TOP BOF project 26824).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Sudeep, P.V., Palanisamy, P., Kesavadas, C. et al. A nonlocal maximum likelihood estimation method for enhancing magnetic resonance phase maps. SIViP 11, 913–920 (2017). https://doi.org/10.1007/s11760-016-1039-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11760-016-1039-6